Problem with fluid simulation, cannot get fluid to move up a thin pipe
There are several options which make fluid simulator fail while finding correct paths for fluid in this case.


Most objects in this scene have scale / rotation unapplied, so just select them all and use options from Ctrl+A menu. In case of fluid simulation, Fluid Sim modifier will not know that the scale of the object was changed if it wasn't applied to the object data. This may lead to unexpected results (same for rotation).
For more info on why is it important to apply them, see Why is it important to apply transformation to an objects data?.  
There is internal face inside of your pipe mesh (assumed to water the big vessel with fluid). The face will effectively prevent fluid from going through the mesh, so delete it.



There are also several double vertices in the mesh, remove them with W > Remove Doubles.  
The pipe, assumed to water the top vessel, consists of several objects; the main pipe has holes where they should connect. This will prevent fluid from coming all the way up to the top vessel because of that hole just in the middle of the main pipe:


Smaller part of the pipe was hidden

To achieve expected results of animation, join these meshes and make them manifold in the place of joint:



Topology is horrible, however at least they are joined and closed. This can be easily done by closing the gap in the main pipe, and using Boolean Union option to join objects effectively.  

The joint between this joined small pipe and big vessel can be left as is - it will only depend on the resolution of the fluid.
The final result will really depend on the bake resolution. If quite low values are used (as 80 or 100), then make sure to scale the pipe a bit up, because otherwise baked fluid will be too fat to flow into it and will just splash in the bottom vessel. You can scale the pipe along normals for that.
Fluid baked on higher values should deal with that (although I don't know how much those values should be as I didn't tested it).